The following table is a partial probability distribution for the MRA Company's projected profits  (x = profit in $1,000s)  for the first year of operation (the negative value denotes a loss). x f(x) −100 0.10 0 0.25 50 0.30 100 0.20 150 0.10 200   (a) What is the proper value for  f(200)? f(200) =  What is your interpretation of this value? This is the  ---Select--- probability percent that the MRA will have a $200,000 profit. (b) What is the probability that MRA will be profitable?   (c) What is the probability that MRA will make at least $100,000?

variable with the following probability distribution. Value x of X P=Xx -20 0.10 -10 0.15 0 0.45 10 0.25 20 0.05 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation EX of X . ?   =EX     (b) Find the variance Var X of X .?   =VarX

The table below shows the probability distribution function of the number of accidents (X) occur in a day by taxis belonging to a taxi company. x 0 1 2 3 4 P(X = x) 0.5 0.15 0.05 2k k (a) Find the value of k.(b) Find the expected value and standard deviation of the number of accidents (X) occurring in a day.(c) Assume the net profit ($), Y, of the taxi company in a day is given by Y = 10000 – 4000X. Find theexpected value, variance, and standard deviation of the net profit of the taxi company in a day.(d) What is the maximum profit the company earn in a day? What is the corresponding probability?(e) What is the probability that the company loses money in a day?(f) Find the probability that there are exactly 3 days that the company loses money in a week (7 days).

The table shows the probability distribution of the number of days (x) to complete a construction project by a contractor.   x f(x) 1 0.104 2   3 0.312 4 0.240 5 0.098 6 0.017   13 If you doubled each number of days to completion in the Days (x) column, the variance of days to completion will be _________.   a 5.710               b 4.758               c 3.965               d 2.855